Mishenichnas Adar time to start learning Hil Purim and Megillah!!!
Tosfos in Megillah 4 asks a similar kashe as tosfos pesachim 43b (today's daf): if we have a principle of "af heim hayu b'oso henes", since women caused or were part of the nes they become obligated in the mitzvos hayom, why do we need a separate limud to teach us that women are obligated in the mitzvah of matzah? Women were the cause of and were certainly part of the shibud and geulah of mitzrayim? Tos. in megillah gives two answers: 1) "af hein" is a sevara that would create a chiyuv derabbanan; the limud creates a chiyuv d'oraysa; 2) without a separate limud, we would have used the gezeirah shava of 15-15 connecting sukkot and pesach to say that just like women are pturos from sukkah, they are pturos from matzah.
Tosfos quotes the opinion of the BH"G that a woman cannot be mozti a man in keri'as hamegillah. Why should that be true - if both men and women have parallel chiyuvim on a derabbanan level, then they should be able to be motzi each other? Rashi in Archin suggests that the BH"G understood that women have only a mitzva of hearing the megillah, not reading it, so the chiyuvim are not parallel. The Aruch haShulchun suggests that the basis for this chiddush is Tosfos's kashe - the fact that we need a limud to teach us that there is a chiyuv of matzah indicates that "af hein" is not equivalent to the chiyuv on men generated by the pasuk!
Achronim give other answers for the BH"G. If one assumes that "af hein" is not more than a din derabbanan, one can distinguish between the chiyuv of a man in mikra megillah, which is divrei kabbalah, and a woman's chiyuv, which is on a lower derabbanan level. This would be a nafka minah between the two deyos of Tosfos's answer.
Two other answers worthy of note: 1) the Brisker Rav suggests that "af hein" is not just a giluy milsa that women are included in the chiyuv of k'rias hamegillah, but is itself the mechayeiv. Based on that, the mechyeiv for men is mikra megillah; the mechayeiv for women is "af hein" and they therefore are not parallel chiyuvim. 2) The gemara later in megillah which asks why there is no hallel on Purim and answers that kri'as hamegillah is a kiyum of hallel on the nes. Based on this, the Marcheshes suggests that a woman can be motzi a man is the chiyuv of mikra, but cannot be motzi him in the additional chiyuv of hallel which she is not obligated in (parenthetically: the Marcheshes writes in his introduction that he does not like the "new" brisker derech halimud that has become popular - a bit of irony that he should discuss two dinim in reading megillah).